The amount of life you lose is determined by the permanent's mana value as it last existed on the battlefield.

If a permanent on the battlefield has {X} in its mana cost, X is 0 for the purpose of determining its mana value.

If the target permanent is an illegal target by the time Feed the Swarm tries to resolve, the spell doesn't resolve. You don't lose any life. If the target is legal but not destroyed (most likely because it has indestructible), you do lose life.